MinT - Best Known (99−56, 99, s)-Nets in Base 8

Best Known (99−56, 99, s)-Nets in Base 8

(99−56, 99, 98)-Net over F₈ — Constructive and digital

Digital (43, 99, 98)-net over F₈, using

t-expansion [i] based on digital (37, 99, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(99−56, 99, 129)-Net over F₈ — Digital

Digital (43, 99, 129)-net over F₈, using

t-expansion [i] based on digital (38, 99, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(99−56, 99, 2500)-Net in Base 8 — Upper bound on s

There is no (43, 99, 2501)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 257275 657213 336980 730405 780177 034985 567446 876260 774850 006181 998826 072360 498281 798250 882216 > 8⁹⁹ [i]